A numerically stable algorithm for two server queue models

In this paper, we consider a queueing system in which there are two exponential servers, each having his own queue, and arriving customers will join the shorter queue. Based on the results given in Flatto and McKean, we rewrite the formula for the probability that there are exactlyk customers in each queue, wherek = 0, 1,…. This enables us to present an algorithm for computing these probabilities and then to find the joint distribution of the queue lengths in the system. A program and numerical examples are given.     

高精度CCD尺寸自动检测系统的光学系统设计

介绍测量精度为±０．００３ｍｍ的ＣＣＤ尺寸检测系统的光学系统设计特点及远心物镜设计原理，并给出了测试结果。     

Tangent cones and Dini derivatives

We prove a property of the Bouligand tangent cone to the epigraph (or to the graph) of a locally Lipschitz function. It is also shown how this result can be used in determining Dini sequences. Finally, some relationships between such a cone and Dini derivatives are provided.     

Hypersurface with Constant Main Curvature Symmetric Functions

ＨｙｐｅｒｓｕｒｆａｃｅｗｉｔｈＣｏｎｓｔａｎｔＭａｉｎＣｕｒｖａｔｕｒｅＳｙｍｍｅｔｒｉｃＦｕｎｃｔｉｏｎｓ￥ＷｕＢａｏｑｉａｎｇ；ＳｏｎｇＨｏｎｇｚａｏ（ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，２２１００９）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，...     

角域上的调和函数与条件Brown运动

设中的角域．该文绘出了A上正调和函数的Martin表示，讨论了极小调和函数与条件Brown运动的一个0—1律之间的关系，并给出了A上极小调和函数的表现形式，     

Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

Cell transfer and monomial positivity

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions. T.L. was supported in part by NSF DMS-0600677.     

Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.